Finance 300Financial Markets

Lecture 11

Professor J. Petry, Fall, 2002©

http://www.cba.uiuc.edu/jpetry/Fin_300_fa02/http://webboard.cites.uiuc.edu/

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HousekeepingEquity projects due.UISES-Investment Challenge Accounts are up.

Log-in and change password.Explore.

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HousekeepingWe have the following information:

– 24 month 9% T-Note, with a yield to maturity of 8.92%. – 6 month, 12 month and 18 month spot rates of 8.0%, 8.3%

and 8.93%.– What will the 24 month spot rate be relative to the 24 month

coupon bond? Why?– Conceptually, how can you find the 24 month spot rate?– What are the steps in that process?

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Duration & VolatilityVolatility

– The tendency of a security price or market index to change due to the changes in market conditions.

• Volatility = Δ price / price

• From the equation above, price movements should be a function of four things:1. 2. 3. 4.

• Three of which are either fixed or predictable.

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tnYdtYd

t PCPRICE

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Duration & VolatilityVolatility

– We have seen enough examples of the inverse relationship between yields and prices. As interest rates move, the price of existing bonds moves in the opposite direction.

– Bond prices, however, do not all move by the same amount:• Example: Suppose you have 2 annual coupon bonds with 5 year

maturities. Market yields for 5 years is currently 7%. – Assume the first bond has a 9% coupon. What is it worth?– Assume the second bond has a 5% coupon. What is it worth?

» Why are they different prices? » Could you predict which would trade at a premium/discount/par?

• Now assume market yields go to 6%, what is each bond worth now?• What are the percent changes in the bonds values? • Which would you have preferred to own?

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Duration & VolatilityDuration

– We often describe this volatility in terms of the “duration” of the bond.

– Duration is the weighted average of the term to maturity of the bond’s cash flows. Duration is also the first order approximation of the slope of the price/yield curve we calculated earlier in the semester. It is directly proportional to volatility.

• If duration is the weighted average of a bond’s cash flows, how does the duration of our 5 year bonds compare to their term to maturity?

• Which has the higher duration? • What is the duration of a 5-year zero coupon bond?• Which of these bonds have the most price risk?

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Duration Calculation

Duration & Convexity Calculation5 year 5% bond (annual coupon payment)

durationyear coupon NPV @ 7% NPV/V NPV/V*t

1 50 46.729 0.051 0.0512 50 43.672 0.048 0.0953 50 40.815 0.044 0.1334 50 38.145 0.042 0.1665 1050 748.635 0.816 4.0786 918.00 1.00 4.52

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Duration Calculation

Duration Calculation5 year 9% bond (annual coupon payment)

durationyear coupon NPV @ 7% NPV/V NPV/V*t

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What is this bond’s duration? What does it mean?